Were dogs a popular pet back then?
Yes, dogs were as big back then as now. Many rich or royal families kept specially bred dogs as companions/pets or as valuable hunting dogs!
The hunting dog here is a formal quotation from the many portraits of the Spanish royal family by Diego Velazquez, who also often depicted his subjects outdoors alongside hunting dogs. Goya, the portraitist here, was obsessed with Velazquez and copied many of his paintings in the then royal collection--now the Prado Museum. The dog here is also an allegory of fidelity; it shows the allegiance of the sitter, Don Tadeo Bravo de Rivero, to the Spanish king, Charles IV.
That portrait by Goya has been in storage for a while and was just recently brought out into the galleries again!
What is the dog's name? Who does he belong to?
Dogs often play an important part in portraiture. We don't know the dog's name, but many wealthy individuals did keep dogs as personal pets. Goya may have included this dog as a traditional symbol of fidelity, suggesting Don Tadeo Bravo de Rivero's devotion to his king.
This portrait shows Don Tadeo's military rank and his social status: he is wearing his cavalry uniform, with a medal pinned to his scarlet jacket. His sword is very elegant, meant more for display than for use. Goya also painted royalty as well as military leaders and wealthy individuals he was very much in demand as a portraitist in his time.
Was Don Tadeo an important person?
Yes, in addition to being a military general, Don Tadeo served as a deputy for the city of Lima in Peru. He and Goya were friends, you can see that the artist signed the painting, "to my friend Don Tadeo Bravo de Rivero" at lower right.